Question

How do you simplify `(c^2+c-56)/(c^2+10c+16)`?

Answer 1

Factor each of the quadratics and eliminate the common factors to find:

`(c^2+c-56)/(c^2+10c+16) = (c-7)/(c+2) = 1 - 9/(c+2)`

with restriction `c != -8`

Explanation:

`(c^2+c-56)/(c^2+10c+16) = ((c+8)(c-7))/((c+8)(c+2)) = (c-7)/(c+2)`

with restriction `c != -8`

The restriction is necessary, because if `c = -8` then both the numerator and denominator of the original expression are `0` so their quotient is undefined, but the simplified expression `(c-7)/(c+2)` is defined when `c = -8`.

Also

`(c-7)/(c+2) = (c+2-2-7)/(c+2) = 1 - 9/(c+2)`